An input-output rule defines how an input value is transformed into an output value. The output is dependent on the input.
Let's illustrate this with an example. Consider the function y = x + 5. According to the reference, in this function, x is the input variable, and y is the output variable. The function operates by taking an input value (x) and producing a corresponding output value (y).
Example
Let's take the input value x = 3.
- Input: x = 3
- Rule: y = x + 5
- Apply the rule: Replace x in the equation with 3: y = 3 + 5
- Output: y = 8
Therefore, when the input is 3, the output is 8.
Input-Output Table
We can represent this relationship in an input-output table:
| Input (x) | Output (y) |
|---|---|
| 3 | 8 |
Other Examples
Here are a few more examples to further clarify the concept:
- If x = 0, then y = 0 + 5 = 5
- If x = -2, then y = -2 + 5 = 3
- If x = 10, then y = 10 + 5 = 15
Each x value you input gives you a different y output based on the rule y = x + 5. This is a clear example of an input-output rule.
